Existence of bounded and unbounded nonoscillatory solutions of nonlinear partial difference equations

摘要

Consider the higher order nonlinear partial difference equation of neutral type A(n)(h)Delta(r)(m) (y(m, n) + cy(m - k, n - l) + F(m, n, y(m - tau, n - sigma)) = 0, (*) where h, r is an element of N(1), k, l, tau, sigma is an element of N(0), c is an element of R and F: N x N x R -> R. In this paper, we first establish the discrete Arzela-Ascoli's theorem. Next, we obtain some sufficient conditions for the existence of bounded and unbounded nonoscillatory solution of Eq. (*). (C) 2006 Elsevier Inc. All rights reserved.